If $A$ is a matrix such that $A^2=I$, then what is the inverse of $A$?

Solution

1. Given the equation $A^2=I$.
2. This can be written as $A\cdot A=I$.
3. By the definition of an inverse matrix, $A\cdot A^{-1}=I$.
4. Comparing the two equations, we see that $A^{-1}=A$.
5. Hence the answer is (A).